Statistics • is the study of the collection, organization, analysis, interpretation and presentation of information or data • all aspects of data including the planning of data collection in terms of the design of surveys and experiments are used

mathematical roots • Two mathematical results of Bayes Theorem are, –THE LAW OF LARGE NUMBERS, and –THE CENTRAL LIMIT THEOREM

law of large numbers (LLN) • Is a theorem • describes the result of performing the same experiment a large number of times • thus the average of results obtained should be close to the expected value, and • The result will tend to become closer to reality

central limit theorem (CLT) • the arithmetic mean of a sufficiently large number of iterates of independent random variables, each with a well-defined expected value and well-defined variance, will be approximately normally distributed • This will probably lead to a conclusion of the reality

normal distribution • suppose – sample contains a large number of observations, – each observation being randomly generated, – in a way that does not depend on the values of the other observations – that the arithmetic average of the observed values is computed, – and if this procedure is performed many times, – then central limit theorem says the computed values of the average will be a “normal distribution“ – The normal distribution is commonly known as a "bell curve"

Bayes' theorem is, • a result that is of importance in the mathematical manipulation of conditional probabilities • It is a result that derives from the more basic axioms of probability • It is a result that can lead to realistic conclusions

Bayesian (or epistemological) interpretation • probability measures a degree of belief • Bayes' theorem then links the degree of belief • in a proposition before and after accounting for evidence. • example, take a proposal that a biased coin is twice as likely to land heads than tails. – Degree of belief in this might initially be 50%. – The coin is then flipped a number of times to collect evidence. – Belief may rise to 70% if the evidence supports the proposition

axioms of probability probability is, • a game of chance • measures the real, physical tendency of something to occur • Measures how strongly one believes it will occur • draws on both these elements? • interprets the probability values of probability theory to answer the above questions

why MH370 flight missing? • Its loss is a mystery • Many theories, probabilities and interpretations still remain • Inconclusive, inadequate and intriguing • Probably Bayes Theoretical approach would help • Scientists tend to believe in this theory as a probable lead to discovery of the missing plane

the theory that would not die • “It’s a very short, simple equation that says you can start out with hypothesis about something - and it doesn’t matter how good the hypothesis is,” • - Sharon Bertsch McGrayne

how because of, • this character of the formula • forcing researchers to change their hypothesis with each new information • that the probability becomes more accurate

the proof • Bayes’ Theorem “allows the organisation of available data with associated uncertainties and computation of the PDF • Scientists applied Bayes’ Theorem in the Air France incident of 2009 • French scientist Pierre Simon Laplace, helped locate German U-boats during World War II and spot Soviet submarines during the Cold War • More recently, it is used in Google's "driverless cars" project and in stock market predictions • PDF or the probability distribution function, identified the target location given these data"

Why Not? • Advocates of this theory said it was also used in the search for the black box of the ill-fated Air France flight 447, which crashed in the vast Atlantic Ocean in June 2009 • What took two years for other experts in the search for the black box, took only five days for consultants who applied the Bayes’ Theorem, to finally find the device 12,000 feet under water. • In the current search for flight MH370, it is “highly unlikely” that Bayes’ Theorem is being applied. Air France Accident summary Date 1 June 2009 Summary Entered high altitude stall, impacted ocean Site Atlantic Ocean near waypoint TASIL [1] 3°03′57″N 30°33′42″WCoordinat es: 3°03′57″N 30°33′42″W Passengers 216 Crew 12 Fatalities 228 (all) Survivors 0 Aircraft type Airbus A330-203 Operator Air France Registration F-GZCP Flight origin Rio de Janeiro–Galeão Airport Destination Paris-Charles de Gaulle Airport

learn from experience • Bayes' Theorem, –is all about learning from experience –one would need "reasonably accurate past experiences" for the theorem to work –in other words, to calculate accurately to locate the plane

find the plane • ‘go find the plane, with science in your bag, enough of spiritual and emotional beliefs and traditional methods’-masi

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